Imperial College London
Portrait Picture

Professor Xue-Mei Li

Faculty of Natural Sciences, Department of Mathematics

Chair in Probability and Stochastic Analysis
 
 
 
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Contact

 

+44 (0)20 7594 3709xue-mei.li Website CV

 
 
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Location

 

6M51Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Gehringer:2022:10.1007/s10959-020-01044-7,
author = {Gehringer, J and Li, X-M},
doi = {10.1007/s10959-020-01044-7},
journal = {Journal of Theoretical Probability},
pages = {426--456},
title = {Functional limit theorems for the fractional Ornstein-Uhlenbeck process},
url = {http://dx.doi.org/10.1007/s10959-020-01044-7},
volume = {35},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeckprocess, providing the foundation for the fluctuation theory of slow/fast systems driven by both long and shortrange dependent noise. The limit process has both Gaussian and non-Gaussian components. The theoremholds for any L2functions, whereas for functions with stronger integrability properties the convergence isshown to hold in the Hölder topology, the rough topology for processes in C12 +. This leads to a ‘roughcreation’ / ‘rough homogenization’ theorem, by which we mean the weak convergence of a family of randomsmooth curves to a non-Markovian random process with non-differentiable sample paths. In particular, weobtain effective dynamics for the second order problem and for the kinetic fractional Brownian motion model.
AU  - Gehringer,J
AU  - Li,X-M
DO  - 10.1007/s10959-020-01044-7
EP  - 456
PY  - 2022///
SN  - 0894-9840
SP  - 426
TI  - Functional limit theorems for the fractional Ornstein-Uhlenbeck process
T2  - Journal of Theoretical Probability
UR  - http://dx.doi.org/10.1007/s10959-020-01044-7
UR  - http://hdl.handle.net/10044/1/84066
VL  - 35
ER  -
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